Tony, if it was Vern you meant, the answer, for those like me devoid of math, is that if you accelerate matter it will get a increasing momentum, or, relative mass as we're talking 'matter' specifically here. That mass building will stop any object of matter from ever being able to expend enough energy to propel itself to the speed of light (in a vacuum).

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Mathematically.

The mass of an object in motion is

m0

m = ----------------

sqrt(1-v2/c2)

where m0 is the rest mass, v is the velocity of the object, and c is the speed of light.

(and sqrt represents the square root function)

As you can see, as v approaches c, v2/c2 approaches 1, and the mass of the object approaches infinity. Clearly an object with infinite mass would be trouble, thus it is speculated that objects with a non-zero rest mass cannot travel faster than light.

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Here. When Vern writes "Gravity slows time. Acceleration has time as a component. Therefore gravity slows acceleration. Then gravity affects gravity the way gravity affects time." I lose it somewhat too?

Gravity definitely slows time, as observed by someone outside that gravitational field, but for those inside it it doesn't. What they will see is that, although their time is as always, the time outside their so called 'frame of reference' aka a neutronstar

f.ex 'speeds up'. but as far as they can measure inside the time they have locally is the same as it was on Earth.

As for acceleration, that is constantly expending energy, as fast as f.ex that ball leaves your hand it has stopped accelerating, be it on Earth or in space. In space it will as you say just 'keep on' uniformly moving until it meets gravitational forces or other hinders. On Earth it will obey gravity and decelerate as it meets the friction of air and gravity, expecting that you throw it with some gusto

There is the argument that you can accelerate down a gravity well though without expending any energy of your own, which contradicts my idea above, as nothing then is seen to expend energy, neither you nor gravity. But acceleration and 'free falling' is to me two different things in that 'free falling' down that gravity well you will be weightless, at all times. At no time will there be any acceleration noticed for you inside that famous 'black box'

. When we discuss all other types of acceleration you will feel 'gravity' tug on you.

The more gravity a object have the more 'acceleration' you might expect. Earth's acceleration due to gravity is 9.8 m/s but the moons is a puny 1.6 m/s (surface). So the more invariant mass (matter) the higher the acceleration as well as gravity.

Gravity and acceleration.===

where

g = acceleration due to gravity (m/s² or ft/s²)

G = universal gravitational constant (m³/kg/s² or ft³/slug/s²)

M = mass of the body (kg or slug)

r = radius of the body (m or ft)

The value of G is known and has been estimated by scientists as:

G = 6.673 x 10-11 m³/kg/s² in the Metric system

G = 3.439 x 10-8 ft³/slug/s² in the English system

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From here. So we can see that gravity does the opposite here, it 'speeds up' the acceleration, as observed inside that 'frame of reference'. But knowing Vern I think he meant something different than this. I know he is well versed in Newtonian Physics, but as it stands I can see that you got confused

As for "On earth and in free space, if I through a ball at the speed of light, time on the ball will slow down, but the ball on earth will slow down and time will turn back to normal, but the one in free space will continue to have the time slowed down until the speed is reduced."

As long as you mean just under the speed of light in a vacuum I'm totally with you. The ball speeding through space will continue to do so, and as seen from an observer at rest with the origin before that acceleration (like being 'still' where you threw it, observing) it will indeed have its 'time' slowed down, as well as now being of an enormous momentum/relative mass. The ball traveling inside Earths gravitational field though, (ah, it will leave it in fact:) but if it didn't, it would be slowed down sooner or later, by the gravitation, or as we physicist aficionados call it 'SpaceTimes Geodesics' bending it, and the friction and gravity slowing it down at the same time.

That shouldn't be read as gravity expends any 'energy' stopping it though. As far as I understands it, it's the other way around, to break free of gravity matter will have to expend energy and if it doesn't have sufficient amounts it will stay inside that gravitational fields center.

As for "As I understand it, gravity slows down time, how does increasingly dense electron flow slow down time?"

A beautiful question that should be answerable too..

So how does it do it? It should, shouldn't it, as observed outside our gravitational field. It sounds like it should increase gravity too? And what about magnetic fields? It's a new one to me

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That link didn't work btw?

So?